In semiconductor fabrication and related technologies, it has become necessary to routinely determine critical dimensions (CD) of physical features, usually in the horizontal dimension, formed in substrates. An example, shown in the illustrative cross sectional view of FIG. 1, includes a trench 10 formed in a substrate 12, such as a silicon wafer. The illustration greatly exaggerates the depth of the trench 10 relative to the thickness of a silicon wafer 12, but the illustrated aspect ratio of the trench 10 is realistic. In advanced silicon technology, the width of the trench may be 0.18 .mu.m; and its depth, 0.7 .mu.m. The critical dimension of the trench 10 may be the width of the top of the trench opening or may be the width of the bottom of the trench 10. In other situations, the depth of the trench 10 is an important parameter. For the dimensions described above, the trench 10 has a high aspect ratio of greater than 4. Although typically sidewalls 14 of the trench 10 have ideal vertical profile angles of 90.degree., in fact the profile angle may be substantially less. Much effort has been expended in keeping the profile angle at greater than 85.degree. or even 88.degree. to 90.degree., but it requires constant monitoring of the system performance to guarantee that such a sharp trench is etched, and substantially lesser angles may be observed if sharp trenches are not required or the process has fallen out of specification. As a result, it has become necessary, either in the development laboratory or on the production line, to measure the profile of the trench 10 with horizontal resolutions of 0.18 .mu.m or even substantially less. Depending upon the situation, the entire profile needs to be determined, or the top or bottom trench width needs to be measured. In other situations, not directly described here, the trench depth may be the critical dimension. More circular apertures, such as needed for inter-level vias, also need similar measurements. Similar requirements extend to measuring the profiles of vertically convex features such as interconnects.
To satisfy these requirements, profilometers based upon atomic force microscopy (AFM) and similar technology have been developed which rely upon the vertical position of a probe tip 20, illustrated in FIG. 1, to measure critical dimension down to the order of tens to hundreds of nanometers. In the past, the probe tip 20 has assumed the form of a conical tip having atomically sized tip dimensions. Such a conical tip has difficulty reaching the bottom of a sharply sloping trench. More recently developed probe tips have a cylindrically or approximately square shaped cross sections of dimensions of 0.2 .mu.m or less. Such a small probe tip is relatively short, of the order of micrometers, and is supported on its proximal end by a more massive tip support.
In the pixel mode of operation, the probe tip 20 is discontinuously scanned horizontally along a line. At multiple positions, which are typically periodically spaced but non-periodic spacing is possible, the horizontal scan of the probe tip 20 is stopped, and it is gently lowered until it is stopped by the surface of the substrate 12. Circuitry to be briefly described later measures the height at which the probe tip stops. A series of such measurements around the feature being probed, for example, on either side of and within the trench 10, provides a profile or topography of the sample.
In the related jumping mode of operation, the probe tip is continuously scanned while it is being lowered to the surface. Once the surface has been encountered, the vertical position of the probe tip is measured, and the tip is then raised during a continuation of the horizontal scan.
An example of such a critical dimension measurement tool is the Model JGCDM-12S available from Surface/Interface, Inc. of Sunnyvale, Calif. It employs technology similar to the rocking balanced beam probe disclosed by Griffith et al. in U.S. Pat. No. 5,307,693 and by Bryson et al. in U.S. Pat. No. 5,756,887. It is particularly useful in the above described pixel mode of operation. The tool is schematically illustrated in the side view of FIG. 2. A wafer 30 or other sample to be profiled is supported on a support surface 32 supported successively on a tilt stage 34, an x-slide 36, and a y-slide 38, all of which are movable about their respective axes so as to provide two-dimensional and tilt control of the wafer 30. Although these mechanical stages provide a relatively great range of motion, their resolutions are relatively course compared to the resolution sought in the probing. The bottom-slide 38 rests on a heavy granite slab 40 providing vibrational stability. A gantry 42 is supported on the granite slab 40. A probe head 44 depends from the gantry 42 through an intermediate piezoelectric actuator providing about 10 .mu.m of motion in (x, y, z). The piezoelectric actuator typically is a thin walled piezoelectric cylinder having separate x-, y-, and z-electrodes attached to the wall of the cylinder to thereby effect separately controlled movement along the three axes. A probe tip 46 projects downwardly from the probe head 44 to selectively engage the top surface of the wafer 30 and to determine its vertical and horizontal dimensions.
Principal parts of the probe head 44 of FIG. 2 are illustrated in orthogonally arranged side views in FIGS. 3 and 4. A dielectric support 50 fixed to the bottom of the piezoelectric actuator 45 includes on its top side, with respect to the view of FIG. 2, a magnet 52. On the bottom of the dielectric support 50 are deposited two isolated capacitor plates 54, 56 and two interconnected contact pads 58, which may be a single long film running between the capacitor pads 54, 56.
A beam 60 is medially fixed on its two lateral sides and electrically connected to two metallic and ferromagnetic ball bearings 62, 64. The beam 60 is preferably composed of heavily doped silicon so as to be electrically conductive, and a thin silver layer is deposited on it to make good electrical contacts to the ball bearings. However, the structure may be more complex as long as the upper surface of the beam 60 is electrically conductive in the areas of the ball bearings 62, 64 and of the capacitor plates 54, 56. The ball bearings 62, 64 are placed on the contact pads 58 and generally between the capacitor plates 54, 56, and the magnet 52 holds the ferromagnetic bearings 62, 64 there. The attached beam 60 is held in a position generally parallel to the dielectric support 50 with a balanced vertical gap 66 of about 25 .mu.m between the capacitor plates 54, 56 and the beam 60 that allows a rocking motion of the 25 .mu.m. Two capacitors are formed between the respective capacitor pads 54, 56 and the conductive beam 60. The capacitor pads 54, 56 and the contact pads 58, electrically connected to the conductive beam 60, are connected to three terminals of external measurement and control circuitry to be described later. The beam 60 holds on its distal end a glass tab 70 to which is fixed a stylus 72 having the probe tip 20 projecting downwardly to selectively engage the top of the wafer 12 being probed. An unillustrated dummy stylus or substitute weight on the other end of the beam 60 provides rough mechanical balancing of the beam in the neutral position.
Three unillustrated electrical lines connect the two capacitor plates 54, 56 and the contact pads 58 to a servo system that both measures the two capacitances and applies differential voltage to the two capacitor pads 54, 56 to keep them in the balanced position. When the piezoelectric actuator 45 lowers the stylus 72 to the point that it encounters the feature being probed, the beam 60 rocks upon contact of the stylus 72 with the wafer 30. The difference in capacitance between the plates 54, 56 is detected, and the piezoelectric actuator 45 withdraws until the capacitance is again equal.
In practice, the determination of the depth (height) of the feature is not so straightforward. Because of electronic noise and the elasticity of both the probing tip and the underlying feature, there is no clear point at which the probe first touches the substrate being probed. For these reasons, it is typical to set a minimum threshold force experienced by the probe at which contact with the underlying feature is established. Such thresholding usually works effectively in the situation in which the probe tip encounters a planar surface because after initial contact, assumed to produce zero force, the force increases very rapidly with continuing downward movement of the probe tip. Solid materials exhibit a high Young's modulus (force vs. compression), that is, they are rigid, and even narrow probe tips exhibit reasonably high rigidity in the vertical direction.
More conventional probe have pyramidal tips with atomically sized tip ends. The typical forces encountered, which are in the range of 10 to 1000 nN, are insufficient to significantly deform or deflect such a tip. However, the situation becomes more complex when, as illustrated schematically in cross section in FIG. 5, a narrow probe tip 20 encounters the sloping sidewall 14. The probe tip 20 may physically encounter the sloping sidewall 14 at a point 80; but, because the probe tip 20 is relatively flexible in the lateral direction, the oblique force exerted on it causes it to bend with the slope of the wall 14 as the tip is further lowered. The flexing problem is intensified by the recently developed very narrow and long probes having diameters of about 10 nm and lengths of about 1 .mu.m because the lateral stiffness of a rod-like probe varies with the fourth power of the probe diameter. Other portions of the apparatus may also move in reaction to the lateral force imparted by the sloping sidewall 14. As a result, the force encountered after initial contact does not increase as quickly as if the encountered surface were planar. The threshold thus may not be exceeded until the probe tip is lowered to a point 82 significantly lower down the sidewall 14. This results in a false measurement of the depth of the sidewall 80 at the original horizontal position of the probe tip 20, or alternatively a false measurement of the horizontal position for such a sidewall depth.
An example of such a depth dependent force experienced by the probe is illustrated in the schematic graph of FIG. 6. As the probe is lowered toward the substrate, there is a substantially constant force signal being observed (the zero point usually being an experimental artifice), as represented by trace 90. The low-force trace 90 is generally flat but substantial noise about a flat response is expected. It is possible that the low-force trace 90 has a linear dependence, either increasing or decreasing slightly, because of instrumental errors. At some point, the probe encounters the substrate, and the force experienced in forcing the probe against the substrate quickly increases, as shown by non-linear trace 92, again with a substantial noise component. For these reasons, a threshold 94 corresponding to force F.sub.T is established that is substantially greater than the noise component and the anticipated linear drift. The measurement is usually stopped after the threshold 94 has been encountered, though it is possible to do some short-period averaging before the threshold comparison to reduce noise. Conventionally, the depth of the probe when the force exceeds the threshold F.sub.T is the experimentally determined depth Z.sub.D.
If the encountered surface is flat, the ascending portion 92 of the data is much steeper than that indicated so the placement of the threshold 94 is not crucial. However, in the illustrated situation for a sloping sidewall and narrow probe tip, the value of determined depth Z.sub.D depends critically on the placement of the threshold 94.
If the trench bottom 84 is encountered between the two points 80, 82, the error is reduced, but in an unknown fashion because the location of the bottom is not known beforehand. Of course, the error illustrated in FIGS. 5 and 6 can be reduced by decreasing the threshold 94 closer to the linear portion 90, but this expedient would reduce the immunity to electronic and other noise.
Accordingly, it is desired to obtain a more accurate method of determining the height of a feature being measured by a force-sensitive probe, such as when a sloping sidewall is expected.